"If you look at what David Cameron says or what (former culture and media Secretary) Maria Miller says and you swap Clarkson for Savile, you get this: David Cameron is effectively saying that Savile's a real talent, Maria Miller saying Savile will be Savile," the source was quoted as saying.

Mr Cameron, who is a close friend of Clarkson, has publicly defended the star, saying his children would be heartbroken if Top Gear was taken off air.

A BBC spokesman said: "To suggest that James Purnell is involved is categorically untrue and ridiculous."

Sources have reportedly tried to pin the blame on another well-known senior executive.

The BBC is holding an internal investigation into Clarkson's "fracas" with Tymon this week and is expected to announce its decision within days.

Although the television show has been taken off air, Clarkson and his co-hosts Richard Hammond and James May are said to be exploring ways in which they can go ahead with a number of upcoming Top Gear Live arena shows and are determined not to disappoint fans who have paid up to £95 for a ticket.